Kinks in the Kondo problem.

We find the exact quasiparticle spectrum for the continuum Kondo problem of k species of electrons coupled to an impurity of spin S. In this description, the impurity becomes an immobile quasiparticle sitting on the boundary. The particles are “kinks”, which can be thought of as field configurations interpolating between adjacent wells of a potential with k + 1 degenerate minima. For the overscreened case k > 2S, the boundary has this kink structure as well, which explains the non-integer number of boundary states previously observed. Using simple arguments along with the consistency requirements of an integrable theory, we find the exact elastic S-matrix for the quasiparticles scattering among themselves and off of the boundary. This allows the calculation of the exact free energy, which agrees with the known Bethe ansatz solution.